An improvement of the Minkowski bound for real quadratic orders using the Markoff theorem

JOURNAL OF NUMBER THEORY

卷:131

Article

Srinivasan, Anitha¹ 

[1] Siddhartha Coll, Mumbai, Maharashtra, India

关键词: Minkowski bound;    Markoff theorem;    Real quadratic order;   

DOI  :  10.1016/j.jnt.2011.02.008

来源: Elsevier

【 摘 要 】

Using the Markoff theorem on indefinite binary quadratic forms it is shown that every element of the class group of any real quadratic order of discriminant d has an ideal of norm less than or equal to 1 + left perpendicular root d/3right perpendicular. This bound is best possible as there are quadratic orders of discriminant d which have ideal classes where the least norm is 1 + left perpendicular root d/3right perpendicular. These discriminants are explicitly given and their connection to the Markoff conjecture is highlighted. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free